7. Operators and functions

Operators act on one or more images as input and produce one or more other images as output. They model image transformations (for example, the Fourier transformation or spatial rotation of an image). In mathematics, an operator (not to be confused with an operation) is an application between two spaces, usually spaces of functions or sets.

Functionals act as an input on one or more images, providing one or more pieces of quantitative information. They model image measurements. In mathematics, a functional is an application of a space (often vector) of functions or a space of sets in the body of scalar (usually real) numbers.

Operators and functionals can be classified into different families, either according to the information they take in as input and provide as output, or according to their type and properties.